A renowned theorem of Blind and Mani, with a constructive proof by Kalai, shows that the whole face lattice of a simple polytope can be determined from its graph. This is part of a broader story of reconstructing face lattices from partial information, first considered comprehensively in Grünbaum's 1967 book. This survey talk includes varied results and open questions by many researchers, on simplicial polytopes, cubical polytopes, zonotopes, crosspolytopes, and Eulerian posets. (Audience members are encouraged to tell me what I have missed!)